Electrical breakdown of anodic aluminum oxide

Results are presented from a study of electrical breakdown of anodic aluminum oxide in a constant field with a platinum pressure electrode. Statistical breakdown parameters and their dependence on the magnitude and polarity of the applied voltage are obtained. Field and temperature dependences of breakdown delay time over the interval 10^–6–10³ sec are determined. It is shown that the experimental (E) curves can be rectified (in two segments) in the coordinates log E^–1. This indicates a possible contribution to the breakdown mechanism by both tunnel injection of electrons from the cathode and subsequent avalanche multiplication of electrons within the dielectric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 25–29, April, 1990.In conclusion, the authors thank T. V. Shmidt and E. Ya. Khanin for assistance in the study.     

Investigation of preheating of laser thermonuclear targets

The preheating level of the thermonuclear fuel and of the gas-compressing shell is the main criterion of the target-compression efficiency in experiments on laserdriven thermonuclear fusion. This paper contains the result of investigations of electronic, radiative, and impact preheating in experiments on compression and heating of hlgh-aspect shell targets in the Del'fin-l laser-derived thermonuclear facility. A procedure, based on analysis of the epithermal emission of the plasma, is considered for measuring the target preheating by fast electrons. The radiative and impact preheating of compressing shells in DD gas are estimated. The results of the investigation demonstrate the high degree of adiabaticity of the compression of the thermonuclear fuel in experiments with the Del'fin-l facility.Nuclear Plasma Laboratory of the Lebedev Physics Institute. Translated from Preprint No. 3, Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.     

Excitation spectrum of anisotropic non-dissipative elastic-plastic medium

The simplest gauge theory of an elastic-plastic medium is considered in this paper that takes account of just translational plasticity. The equations of motion for such a model turn out to be linear and permit the normal modes spectrum of a medium to be obtained. Taking account of plasticity results in a cardinal transformation of the elastic branches of the spectrum and the appearance of a group of plasma oscillations of a dislocation gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 64–68, June, 1990.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

Elliptic bundle and generating operators

A hierarchy of Poisson Hamiltonian structures connected with an elliptic spectral problem is constructed. Generating operators connected with the Landau-Lifshits equations and asymmetric chiral 0(3)-field are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 76–87, 1987.The author is profoundly grateful to P. P. Kulish, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the present paper and helpful comments.     

Singular parts of contractive analytic operator functions

One considers the class _G of holomorphic functions in a domain G, whose values are contractions in a separable Hilbert space. It is proved that if T(·) _G , T(z₀) is a weak contraction, its singular part T^s(z₀) is complete, and the increments T(z)–T(z₀) are not too large (for example, finite-dimensional), then the operator T^s(z₀) is complete for almost all zG. If, however, T(z₀) is, in addition, completely nonunitary and satisfies definite smoothness conditions, then in the nontrivial case the spectrum [z] of the contraction T^s(z) (zG) is a thin set: The proof of the mentioned results is based on the investigation of the formulas obtained in the paper, connecting the characteristic functions of the contractions T(z) for different values of zG.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 30–44, 1987.     

Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

Bahadur effectiveness of Watson-Darling goodness-of-fit tests

The rough asymptotic behavior of the probability of large deviations is found for Watson-Darling goodness-of-fit tests, which are centered versions of Kolomogorov-Smirnov statistics. Their Bahadur effectiveness is calculated and conditions for local asymptotic optimality for the alternative of translation are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 138–145, 1987.